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A352625 A (25,-29) Somos-4 sequence. 0

%I #8 Mar 27 2022 13:41:23

%S 1,2,7,59,1529,83313,7869898,1687054711,1123424582771,

%T 1662315215971057,4257998884448335457,23385756731869683322514,

%U 397068399296019032727466599,15886280085653574502219650145963,1107464108502549897934954766675333353,157131202095317153373302215985417166354641

%N A (25,-29) Somos-4 sequence.

%C Hankel transform of A188314 with first term omitted.

%F a(n) = (25*a(n-1)*a(n-3) - 29*a(n-2)^2)/a(n-4) for all n in Z.

%F a(n) = (29*a(n-1)*a(n-4) - 13*a(n-2)*a(n-3))/a(n-5) for all n in Z.

%F a(n) = b(1-2*n) = b(2*n+2) = A188313(-1-n) for all n in Z where b(n) = A006720(n).

%e G.f.: 1 + 2*x + 7*x^2 + 59*x^3 + 1529*x^4 + 83313*x^5 + ...

%e a(2) = 7 = 2*16 - 5*5 = det([2, 5; 5, 16]).

%t b[ n_] := If[OddQ[n], a[-(n-1)/2], a[n/2-1]]; a[ n_] := If[-3<=n<=1, {23, 3, 1, 1, 2}[[n+4]], 2*b[1-n]^3*b[2-n] + b[-n]^2*(b[2-n]*b[3-n] - b[1-n]*b[4-n])];

%Y Cf. A006720, A188313, A188314.

%K nonn

%O 0,2

%A _Michael Somos_, Mar 24 2022

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Last modified May 18 03:43 EDT 2024. Contains 372618 sequences. (Running on oeis4.)